No, but certification is required through regional, non-profit agencies.
While not a governing body, Department of Social Services' Office of Deaf Access: Deaf Access Program ensures that State and local government programs are adapted to meet the communication needs of individuals who are deaf and hard of hearing. CA Dept. of Education governs Educational Interpreters.
By July 1, 2009, and thereafter, an educational interpreter shall be certified by the national RID, or equivalent; in lieu of RID certification or equivalent, an educational interpreter must have achieved a score of 4.0 or above on the EIPA, the ESSE-I/R, or the NAD/ACCI assessment. If providing Cued Language transliteration, a transliterator shall possess TEC Unit certification, or have achieved a score of 4.0 or above on the EIPA - Cued Speech. According to Department of Social Services: An interpreter should be certified by either the Registry of the Interpreters for the Deaf (RID), the National Association of the Deaf (NAD) or the American Consortium of Certified Interpreters (ACCI).
There is a waivor for not meeting the standards.